Maybe he realizes the exam is too dangerous or he discovers some unfairness in it. In the original Naruto story, Naruto has faced many difficulties and moral dilemmas during the Chunin Exam. So in the fanfiction, similar situations might push him to quit.
He might face disappointment from his friends and mentors. His friends who were also participating in the exam might feel let down, and his mentors, like Kakashi, could be concerned about his decision and how it will affect his future as a ninja.
Well, in the fanfic, there might be new and unexpected opponents. Maybe some characters who were not that prominent in the original chunin exam could have a big role this time.
Perhaps he was tricked into quitting. There could be some villains in the fanfiction who managed to deceive Naruto into believing that quitting was the best option for him. They might have used his naivete against him. For example, they could have told him that by quitting he was protecting his friends, when in fact they just wanted him out of the competition.
Maybe in a fanfic, Naruto is dealing with a personal crisis or a family matter that makes him unable to attend the Chunin Exam. Or perhaps there's a magical curse that keeps him away from it.
There's also a chance that a new character could be the main character in the fanfic. Maybe someone who has a special connection to the chunin exam, like a character from a minor clan who has a hidden power and wants to prove himself during the second chunin exam.
One possible fanfiction could be about Sakura showing off her improved medical ninjutsu skills during the Chunin Exam. She might use her skills to quickly heal her teammates during battles, surprising everyone with her growth.
It could be quite challenging for them. Without Naruto's unique skills and strategies, they might have to rely more on their own teamwork and individual strengths.